Estimation of N*0 for the Two-Scale Gamma Raindrop Size Distribution Model and Its Statistical Properties at Several Locations in Asia

Abstract

An automatic estimation method is developed to detect stepwise changes in the amplitude parameter of the normalized raindrop size distribution (DSD) N*0. To estimate N*0, it is also assumed that the variation of three DSD parameters follows the two-scale gamma DSD model; this is defined as a DSD model in which one DSD parameter is fixed, the second is allowed to vary rapidly, and the third is constant over a certain space or time domain and sometimes exhibits stepwise transitions. For this study, it is assumed that N*0 is the third DSD parameter. To estimate this stepwise-varying parameter automatically, a non-Gaussian state-space model is used for the time series of log10N*0. The smoothed time series of log10N*0 fit well to the stepwise transition of log10N*0 when it was assumed that the state transition probability follows a Cauchy distribution. By analyzing the long-term disdrometer data using this state-space model, statistical properties for log10N*0 are obtained at several Asian locations. It is confirmed that the N*0 thus estimated is useful to improve the rain-rate estimation from the measurement of radar reflectivity factor.